Hi Amin Darvishi

Calculating binary interaction parameters (BIPs) is a crucial part of understanding the behavior of mixtures in thermodynamics, particularly in the context of equations of state. BIPs are usually determined through experimental data fitting procedures.

The best way to calculate binary interaction parameters is to use experimental phase equilibrium data (like VLE, LLE, and SLE) along with an equation of state (EoS), such as the Peng-Robinson or Soave-Redlich-Kwong EoS. By minimizing the discrepancies between the calculated and experimental phase behavior, you can estimate the BIPs.

To estimate BIPs in MATLAB, you can use optimization functions such as fmincon or lsqnonlin. Here's a simplified example of how you might set up such a problem using fmincon:

MATLAB CODE :

% Define the objective function

objfun = @(bip) sum((vle_exp - vle_calc(bip)).^2);

% Initial guess for BIPs

bip0 = [0, 0];

% Use fmincon to minimize the objective function

options = optimoptions('fmincon','Display','iter');

bip = fmincon(objfun, bip0, [], [], [], [], [], [], [], options);

In this example, vle_exp is the experimental VLE data, vle_calc is a function that calculates VLE data given BIPs, and bip is the BIPs. The function fmincon is used to minimize the sum of squared residuals between experimental and calculated VLE data.

Please note that this is a simplified example. The actual implementation would require a more complex function vle_calc that calculates phase behavior using a specific equation of state, and possibly additional constraints in the call to fmincon to ensure physical meaningfulness of the BIPs.

Unfortunately, due to the complexity and specific nature of such calculations, a universally applicable MATLAB code is not available. The actual code would depend on the specific EoS used, the type of phase equilibrium data, and the specific compounds being considered. You may need to consult with a thermodynamics textbook or a chemical engineer for a more detailed and accurate method for calculating BIPs for your specific use case.

with Best wishes